Recently it was reported in newspapers that CBSE moderates its marks by effectively increasing them – largely to “compete” with other Boards. It was also reported recently that some of the top colleges in Delhi have a majority of students from one Board in south, and a large number from one school.

Both of these anomalies are due to one reason – admission being based on Board percentage without normalizing the marks of different Boards. Due to this, Boards realize that their students will benefit if they have a higher percentage – so there is a race to give more marks. Besides distorting the admission process, this race is unhealthy for education and learning and gives a false sense of achievement to students.

Of course the natural course of action is to normalize marks from different Boards. Normalization across Boards can be easily done – all it requires is a little extra information from each Board. For some strange reason, it has not become regular practice and Boards do not provide sufficient information for normalization.

Let us first understand the normalization problem. Each Board gives marks between 0-100%. Normalization requires that marks between 0-100 given by different Boards be converted to a “normalized score”, also between 0 and 100, which provides a common reference where X marks mean the same, regardless of whether the Board was “tough” or “easy” in its marking.

One approach to normalize, which CBSE also used for JEE, is to base it on the percentile of a student in the Board. The percentile score of a student reflects what percentage of students in the Board have marks below that of the student. I.e. a student with 90 percentile means that 90% of the students have received marks that are below this student’s marks. To convert marks to percentile score, students are ordered in the order of marks they received, and then divided in 100 equal groups – the top 1% students fall in 99-percentile, the next 1% fall in 98-percentile, etc. (This can, of course, be done at 0.1 or 0.01 percentile granularity for finer resolution.) Once percentile is given, then there are ways to normalize, with the assumption that top N% of the students in a Board are essentially similar to top N% students in another Board, i.e., a 99 percentile student in one Board can be considered similar to a 99 percentile student of another Board. (If this assumption cannot be made, then it will require calibrating different Boards – an exercise that is unlikely to be undertaken, and if initiated, unlikely to culminate in an acceptable calibration.)

With a percentile score, one way to normalize across Boards is simply to use the percentile score. In this case, a student with 99.5 percentile (from any Board) will be ranked higher than a student in 99.3 percentile (from any Board). The percentile score can have finer granularity, if desired, and within each percentile, there can be tie-breaking rule.

The ranking with percentile is sufficient if the decision of admission is based only on class XII score, i.e. one needs to rank or order students only on class XII score. However, if admission is based on sum of multiple scores, in which one of them is the class XII marks (as was the case in JEE, where 60 marks came from JEE exam and 40 from class XII), then the situation is more complex and percentile will have to converted to a normalized score to be added to the other scores.

There are techniques to convert the percentile score to a normalized score. For this conversion, a desired target distribution is needed, which gives what fraction of students should be at each mark in the normalized marks between 0-100. The target distribution for normalized marks is a choice to be made, and any reasonable distribution can be chosen – the preferred distribution for exams is Normal Distribution, in which the largest fraction of students is at the mean and then the fraction at each mark reduces as we move on the two sides of the mean. If the target distribution is taken to be Normal Distribution with mean of 50 and the standard deviation (a statistical attribute indicating the variability in scores) of 15, then 99 percentile will translate to 85 normalized marks, 98 percentile to 81 marks, 95 percentile to 75 marks, 90 percentile to 69 marks. There are standard tables available for this conversion. (This conversion will be different if a different mean and/or standard deviation are selected.)

It should be clear that with percentile based normalization, inflating marks in a board does not help students – the top 1 % students of all boards will be mapped to the same normalized marks. So, in a Board which has inflated marks such that a large fraction of its students get above 90% marks, only the top 1% students will get the same normalized score (99 percentile, or 85 marks in the above example), which will be same as the top 1% students from a Board which has a much smaller fraction of students above 90%.

Overall, normalization can be done easily and transparently if information about percentile of a student is provided by the Boards.  If Boards provide the percentile, normalization is straightforward.

Normalization is not possible if Boards only give the percentage marks to students, as they do now. Though determining percentile is trivial and Boards can easily do it, for some reason, it is not being done. Perhaps because just with marks a Board can have as many students above 90% as it wants and let the students and their parents feel good. With percentile only 10% of the students can be in the 90 percentile – which will give a clear picture to the student about his/her relative standing in the Board. Given this situation, probably MHRD will have to mandate that percentile information must also be provided to the students. And to support this move, all universities that use class XII marks for admission can declare that they will normalize marks of different Boards and will therefore not admit students from a Board unless the percentile scores are also made available – if this is done all Boards will have to provide this information.

If normalization is done, besides fairness in admissions, it will also lead to curtailing of the unhealthy exercise of marks inflation that the boards seem to have gotten into. If normalization is not done, given the publicity received about DU’s admission this year, we will see an unhealthy race between Boards to give easy marks, resulting in a complete failure of merit based admissions, with less deserving students from some Boards getting admission into the best colleges in the country at the cost of more deserving students from some other Boards being denied admission.